### Hooke's Law

Laboratory 52 investigated Hooke's Law using readily available local materials, styrofoam cups, marbles, and elastic bands. This laboratory substitutes the traditional springs and masses, both of which are unavailable in the local schools, with elastic and marbles. I note to the students that if they have no mass balance, and no public school does out here as far as I now, just use five grams per marble. Essentially one is measuring in marble units.

The elastic is common dress elastic, attached via lengths of string or yarn to overhead hooks. Noting that schools also lack meter sticks, I recommend dropping the cup lower and using rules. Typical cup descents are less than 30 cm.

Betsyna measures the extension.

This spring the students massed all thirty marbles at one time. This term the mass of the cup was not an issue as it had been last fall. All thirty marbles fit in the mass balance pan. This led to a further modification at 8:00. I had the students round to the nearest whole gram that was a multiple of three. Dividing by thirty marbles left only a single decimal place and no repeating decimals.

Sylvia, Antoinette, and Fritz analyze their data

Last fall the divided answer had been round to the nearest tenth, this does the same thing but handles the rounding beforehand. I also used this opportunity to teach/reteach the rule that one can add the digits to find a multiple of three.
Tracy Anne measures the extension of the elastic, Annalyn and Betsyna in the background

Most of the sets of thirty marbles massed between 150 grams and 160 grams. Thus a 152 gram set of thirty was rounded to 153 grams prior to dividing by thirty. The resulting errors are small and are, quite frankly, dwarfed by measurement errors.
Ardos Ardos, Lilyann, and Brilinda working on their data

The above process, first used fall 2010, removed the need to mass each marble individually, which had been time consuming and interrupted the process of observing the elastic stretch.
That fall I noted that after seeing data for this lab over the previous three terms I had come to realize that small differences in marble mass were not significantly affecting the the data. The elastic behaves non-linearly at times, and this can be better seen in the faster, more efficient process developed fall 2010.

The elastic is only somewhat linear and actually behaves in a somewhat complex manner that varies with the length. This provides fertile ground for discussions with groups of their data, although this is generally only possible with groups that have a lap top with which to chart the data. Hand drawn graphs rarely capture the subtle S curves that are often encountered in the this laboratory.

This term this is only the third lab that gets handed in, and the first lab that does not feature a post-lab session upstairs.